#### Answer

$x=4$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
To solve the given equation, $
\log_2(\log_2 x)=1
,$ change to exponential form. Then do checking of the solution/s with the original equation.
$\bf{\text{Solution Details:}}$
Since $\log_by=x$ is equivalent to $y=b^x$, the equation above, in exponential form, is equivalent to
\begin{array}{l}\require{cancel}
\log_2 x=2^1
\\\\
\log_2 x=2
.\end{array}
Converting to exponential form again, the equation above is equivalent to
\begin{array}{l}\require{cancel}
x=2^2
\\\\
x=4
.\end{array}
Upon checking, $
x=4
$ satisfies the original equation.